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Simplifying 9k2 + -9k + -40 = 0 Reorder the terms: -40 + -9k + 9k2 = 0 Solving -40 + -9k + 9k2 = 0 Solving for variable 'k'. Factor a trinomial. (-5 + -3k)(8 + -3k) = 0Subproblem 1
Set the factor '(-5 + -3k)' equal to zero and attempt to solve: Simplifying -5 + -3k = 0 Solving -5 + -3k = 0 Move all terms containing k to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -3k = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3k = 0 + 5 -3k = 0 + 5 Combine like terms: 0 + 5 = 5 -3k = 5 Divide each side by '-3'. k = -1.666666667 Simplifying k = -1.666666667Subproblem 2
Set the factor '(8 + -3k)' equal to zero and attempt to solve: Simplifying 8 + -3k = 0 Solving 8 + -3k = 0 Move all terms containing k to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3k = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3k = 0 + -8 -3k = 0 + -8 Combine like terms: 0 + -8 = -8 -3k = -8 Divide each side by '-3'. k = 2.666666667 Simplifying k = 2.666666667Solution
k = {-1.666666667, 2.666666667}
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